## 19 Jul Carnival of Mathematics #124

I am very pleased to be the hosting the 124th edition of the Carnival of Mathematics, organised every month by the awesome people at The Aperiodical. Following tradition, I would try to say something interesting about the number 124.

The usual properties of **124** are that it is composite and even. 124 is the sum of eight consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29). It is a nontotient since there is no integer with 124 coprimes below it, it is an untouchable number since there is no integer whose proper divisors add up to 124. The number n is *deficient* if the sum of all its positive divisors except itself is less than n, and 124 is such a number.The number n is *odious* if it has an odd number of 1's in its binary expansion and 124 is an odious number.

Now, for some more interesting properties of the number. It is a repunit in base 5, that is in base 5 the number is written as 444 which is just a repetition of the same digit more than once with no other digits. 124 is the smallest number with the property that its first 3 multiples contain the digit 2.

Without further ado, let me list the submissions that we recieved:

- John Cook has written about the mystery curve and has provided links to many related posts.
- Wired has a nice article about internet art which is inspired by mathematics.
- In a similar vein, here is another one about art and mathematics.
- A very interesting way of visualizing the factorizations of 100 can be found here.
- Euler's number is the protagonist of this short article about some of its properties.
- Scientific American has a nice blog post on the most mathematically perfect day.
- Ganit Charcha has a very well written post about the divisor function which would be very helpful for beginning elementary number theory students.
- An interview with Nira Chamberlain about how math is not just a tool for use but a confluence of beautiful ideas.
- Two comics on the occasion of Day and 4th of July.
- Daniel McQuillan writes about some famous inequalities in mathematics and the intuition behind them.
- An interview with Siobhan Roberts, the author of John Conway's biography.
- Here is a deceptively simple paradox from the financial arena.
- John Cook writes about integers whose last digit do not change when raised to the fifth power.
- Finally, an interesting mathematical puzzle created by Colin Beveridge.

Thanks to everyone who sent us the submissions, I had a great time hosting this carnival. The next carnival in August 2015 will be hosted by Nick at Data Genetics.

#### Manjil Saikia

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